Math 1A – Chapter 2 Test – Fall ’04     Name:_________________________________

Show your work for credit.  Write all responses on separate paper.  Do not abuse a calculator.

1.      Consider

a.       Approximate the value of  at x = 64.001 and 63.999 – what do your results suggest about ?

b.      How close does x have to be to 64 to ensure that the function is within 0.1 of it’s limit?

 

2.      Is there a number a such that   exists?  If not, why not?  If so, find the value of a and the value of the limit.

3.      Consider .

a.       What theorem is essential to evaluating this limit.  Why are the conditions of the theorem met?

b.      Use the theorem to evaluate the limit.

4.      For the function g whose graph is shown, approximate the following, writing “DNE” if the limit doesn’t exist and  or , as appropriate. 

a.	b.	c.
d.	e.	f.

 

5.      Suppose the height H of an object (in meters) at time t (in seconds) is given by

a.       What is the average velocity over the interval

b.      Find an interval over which the average velocity of the object is a 1000 m/s.

6.      Let B(t) be the number of Elbonian buffalo per capita at time t.  The table below gives values of B(t) as of June 30 of the specified year.  What is your best approximation to the value of ?                

7.      Consider the function .

a.       Use the definition of the derivative to show that .

b.      Find an equation for the line tangent to x(t) where t = 1.

c.       Use a linear approximation to approximate x(1.05)

8.      For the function  whose derivative function  is graphed below, find where:

a.        is increasing

b.       is concave up

c.        has a local maximum.

d.       is positive.

e.       .